where \(w_{ij}\)  is a fundamental tensor in our part
of the Universe (odd powers of \(k_i\)  would contradict
commutativity of the Gaussian random field \(\delta ({\bf k})\) ,
see Eq. (REF )). Such a dependence would definitely
imply
that the Universe was anisotropic at the
pre-hot stage, when the primordial
perturbations were generated. This statistical anisotropy
is rather hard to obtain in inflationary models, though it is
possible in inflation with strong vector fields [1]}, [2]}, [3]}.
On the other hand, statistical anisotropy is
natural in some other scenarios, including conformal
models [4]}, [5]}.
The statistical anisotropy
would show up in correlators [6]}, [7]}
\(\langle a_{ lm} a_{ l^{\prime } m^{\prime }} \rangle \;\;\;\;\;\; \mbox{with}~~{ l^{\prime }\ne l}~~\mbox{and/or}~~{ m^{\prime } \ne m}.\) 
